An Elementary Course in Synthetic Projective Geometry


by Lehmer, Derrick Norman




Edition 1, (November 4, 2005)





PREFACE


The following course is intended to give, in as simple a way as possible,
the essentials of synthetic projective geometry. While, in the main, the
theory is developed along the well-beaten track laid out by the great
masters of the subject, it is believed that there has been a slight
smoothing of the road in some places. Especially will this be observed in
the chapter on Involution. The author has never felt satisfied with the
usual treatment of that subject by means of circles and anharmonic ratios.
A purely projective notion ought not to be based on metrical foundations.
Metrical developments should be made there, as elsewhere in the theory, by
the introduction of infinitely distant elements.

The author has departed from the century-old custom of writing in parallel
columns each theorem and its dual. He has not found that it conduces to